This is a pilot study designed to evaluate the toxicity of a five-day infusion of paclitaxel concurrent with radiation therapy for advanced head and neck cancers. Patients with previously untreated stage III and IV squamous cell cancer of the oral cavity, oropharynx, hypopharynx, larynx, and maxillary sinus as well as stage II squamous cell cancers of the base of tongue and maxillary sinus are eligible. Tolerance of the regimen will be evaluated by using RTOG and CTEP standard toxicity criteria and by median elapsed treatment time. Serial tumors will be obtained to measure tumor potential doubling time and biological effects of treatment on the cell cycle.